Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces

• URL: http://arxiv.org/abs/2605.28106v1
• Date: Wed, 27 May 2026 07:58:49 GMT
• Title: Gaussian Processes with Sample Paths in Reproducing Kernel Banach Spaces
• Abstract summary: We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces.<n>Building on these results, we extend the classical Driscoll theorem to the Banach space setting.
• Score: 1.7532045941271799
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We investigate the connection between Gaussian processes and Gaussian random elements in reproducing kernel Banach spaces. We show that the covariance operator of a weak second-order Radon probability measure on such a space is uniquely determined by a positive definite function. In the Gaussian case, we characterize those positive definite functions that arise from covariance operators in terms of $γ$-radonifying operators. Building on these results, we extend the classical Driscoll theorem to the Banach space setting.

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